Generalized two-step Maruyama methods for stochastic differential equations

Abstract In this paper, we propose generalized two-step Maruyama methods for solving Ito stochastic differential equations. Numerical analysis concerning consistency, convergence and numerical stability in the mean-square sense is presented. We derive sufficient and necessary conditions for linear mean-square stability of the generalized two-step Maruyama methods. We compare the stability region of the generalized two-step Maruyama methods of Adams type with that of the corresponding two-step Maruyama methods of Adams type and show that our proposed methods have better linear mean-square stability. A numerical example is given to confirm our theoretical results.

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